Question

equilateral triangle abc has a perimeter of 96 millimeters. a perpendicular bisector is drawn from angle a to side bc at point m. what is the length of mc? 16 mm 24 mm 32 mm 48 mm

Explanation:

Step1: Find side - length of equilateral triangle

Since the perimeter $P$ of an equilateral triangle is $P = 3s$ (where $s$ is the side - length) and $P=96$ mm, then $s=\frac{P}{3}=\frac{96}{3}=32$ mm.

Step2: Use property of perpendicular bisector in equilateral triangle

In an equilateral triangle, a perpendicular bisector from a vertex to the opposite side bisects that side. If the side length of $\triangle ABC$ is 32 mm and $M$ is the mid - point of $\overline{BC}$, then $MC=\frac{BC}{2}$. Since $BC = 32$ mm, $MC = 16$ mm.

Answer:

A. 16 mm